"Harlan Grove" wrote:

> Will wrote...
> ....
> >With regards to the given solution, some steps are unclear, for example, why
> >a column of 1s is added and why the columns are switched around, hence the
> >explanation is not sufficiently clear in order to generalise. . . .
>
> Let me try again. The explanation is clear to anyone who knows the
> linear algebraic form of the least squares and maximum likelihood
> estimators and how to implement them brute force in Excel. It can be
> generalized, but you'd need to be very familiar with Excel array
> formulas and matrix arithmetic functions. I'm not deliberately trying
> to be derogatory (some would say it just comes naturally, but I
> digress), but if you don't see how to generalize the approach in the
> Microsoft KnowledgeBase, then you wouldn't be likely to be able to spot
> problems in an Excel implementation of QR decomposition.

To answer my own question above, the reason for the column of 1s in the
knowledge base article is that the regression using QR decomposition is of
the form Rx = Q[T]b, so the regression is fitting a coefficient to a unit
value, which is equivalent to solving for the constant term based on the
usual construction of y=ax + b. A better description of what's going on
(which would have made the knowledge base article far more useful and
understandable) is available at
http://en.wikipedia.org/wiki/Linear_least_squares
>
> You may need a fully constructed workbook implementation of QR
> decomposition. I'm not aware of any available on the web, but others
> may.
>
> > . . . I am trying to
> >generate an Excel-based solution for some econometrics tests (specifically,
> >the Augmented Dickey-Fuller test which is specifically designed to account
> >for correlations in the lagged variables, and hence is guaranteed to generate
> >problems with multi-collinearity) and I would rather not be forced down the
> >route of switching to using Matlab instead of Excel.
>
> You shouldn't be using Excel for this. Even Excel 2003 has its
> weaknesses, and rolling your own QR decomposition template would result
> in a less efficient and less robust (in the software sense, not the
> statistical sense) tool than most dedicated stats packages.
>
> There are much cheaper alternatives than MATLAB. There are addon
> packages for R and gretl that calculate augmented Dickey-Fuller tests,
> and both R and gretl are GNU software packages. There may also be time
> series add-ins for Excel that provide this test and cost less than
> MATLAB. Dunno.
>
>